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It is rigorously proved that the analog of free energy for the percolation models has a singularity at zero external field as soon as percolation appears. The singularity is an essential one at least for large concentrations. Results on the asymptotic behavior of the cluster-size distribution are also obtained for percolation models and for the Ising model at low temperatures.
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Kunz et al. (1978) studied this question.
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